[HDU2588]GCD 欧拉函数
2017-10-14 20:09
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GCD
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 2437 Accepted Submission(s): 1253(a,b) can be easily found by the Euclidean algorithm. Now Carp is considering a little more difficult problem:
Given integers N and M, how many integer X satisfies 1<=X<=N and (X,N)>=M.
Input The first line of input is an integer T(T<=100) representing the number of test cases. The following T lines each contains two numbers N and M (2<=N<=1000000000, 1<=M<=N), representing a test case.
Output For each test case,output the answer on a single line.
Sample Input 3 1 1 10 2 10000 72
Sample Output 1 6 260
Source ECJTU 2009 Spring Contest
Recommend lcy 题目大意:求sigma (i=1--n)gcd(i,n)>=m的数的个数 题解: 问题sigma(i=1--n)gcd(i,n)>=m的数的个数,设d=gcd(i,n), 根据题目的要求d>=m&&d|n. 所以我们要求sigma(d>=m&&d|n)sigma(i=1--n)gcd(n,i)==d 变形就是sigma(d>=m&&d|n)sigma(i=1--n)gcd(n/d,i/d)==1的数 的个数,那么d是枚举的,n/d是已知的,gcd(n/d,i/d)==1的个数 就是phi(n/d)。 代码:hdu炸了没测
#include<iostream> #include<cstdio> #include<cstring> using namespace std; int t,n,m; int euler(int x){ int ret=x; for(int i=2;i*i<=x;i++){ if(x%i==0){ ret=ret/i*(i-1); while(x%i==0)x/=i; } } if(x>1)ret=ret/x*(x-1); return ret; } int main(){ scanf("%d",&t); while(t--){ scanf("%d%d",&n,&m); int ans=0; for(int i=1;i*i<=n;i++){ if(n%i==0){ // cout<<euler(n/i)<<" "<<euler(i)<<endl; if(i>=m)ans=ans+euler(n/i); if(n/i>=m&&i*i!=n)ans=ans+euler(i); } } printf("%d\n",ans); } return 0; }
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